Studies in Applied Mathematics最新文献

{"title":"Local Well-Posedness for the Biharmonic Nonlinear Schrödinger Equation in Low Dimensions","authors":"Iryna Petrenko,&nbsp;Oscar Riaño,&nbsp;Svetlana Roudenko","doi":"10.1111/sapm.70278","DOIUrl":"https://doi.org/10.1111/sapm.70278","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper we consider the fourth-order (or biharmonic) nonlinear Schrödinger (NLS) equation in dimensions 1, 2, and 3, where the potential term is expressed as a power nonlinearity (for any positive power) and the dispersion operator has the <i>fourth</i>-order combined with the lower <i>second</i>-order. The fourth order NLS equation has recently attracted the attention of researchers since quartic solitons have been experimentally obtained in optics, and thus, the mathematical theory of solutions to the fourth-order NLS equation in physical dimensions <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$N=1,2,3$</annotation>\u0000 </semantics></math> is timely to develop. In this work we show the local well-possesses of the fourth-order or biharmonic NLS equation on a weighted subset of a Sobolev space as well as in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>s</mi>\u0000 </msup>\u0000 <annotation>$H^s$</annotation>\u0000 </semantics></math> spaces.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discrete Breathers in a Honeycomb Lattice Near a Semi-Dirac Point","authors":"Andrew Hofstrand","doi":"10.1111/sapm.70282","DOIUrl":"https://doi.org/10.1111/sapm.70282","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the dynamics of discrete breathers—spatially localized and time-periodic solutions—inside the bandgap of a nonlinear honeycomb lattice where the dispersion landscape approaches a so-called semi-Dirac point in which the bands cross linearly in one direction and quadratically in the orthogonal direction. By studying breather dynamics in two opposing asymptotic regimes, near the continuum and anti-continuum limits, we capture the spatial profiles of hybrid coherent structures having central cores supported on a finite number of lattice sites and infinite decaying tails that are well approximated by exact separable solutions to an effective long-wave PDE theory at spatial infinity. We find that these breathers are dynamically stable over a wide range of parameters and find an instability transition. Finally, we analyze the Floquet stability of spatially extended nonlinear plane waves bifurcating from the zero solution at the edges of the gap and how they shape breather profiles inside the gap.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blow-Up Criteria for the 1D NLS With Combined Nonlinearities","authors":"Alex D. Rodriguez","doi":"10.1111/sapm.70272","DOIUrl":"https://doi.org/10.1111/sapm.70272","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we develop two different types of criteria for the finite time blow-up solutions to the combined nonlinear Schrödinger equation in 1D. The first one is a negative energy criterion developed for triple combined nonlinearity and then for a (convergent) infinite sum of combined nonlinearities, including an exponential nonlinearity. The second one is a positive energy criterion for the double nonlinearity with the defocusing–focusing coefficients. We also provide examples of initial data that satisfy either of the criteria.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite Ion Size and Permanent Charge in a Poisson–Nernst–Planck Ion Channel Model: Existence and a Critical Potential Phenomenon","authors":"Hamid Mofidi,&nbsp;Jie Song,&nbsp;Mingji Zhang","doi":"10.1111/sapm.70281","DOIUrl":"https://doi.org/10.1111/sapm.70281","url":null,"abstract":"<div>\u0000 \u0000 <p>We consider a quasi-one-dimensional Poisson–Nernst–Planck (PNP) model of ionic transport through a membrane channel, incorporating two oppositely charged ion species, nonzero permanent charge distributions, and nonuniform finite ion sizes modeled via hard-sphere potentials. First, we establish a rigorous existence and local uniqueness result for the steady-state PNP system using geometric singular perturbation theory, treating the finite ion sizes as small parameters. Second, we conduct a detailed asymptotic analysis of zero-current ionic flows for small permanent charge. This analysis reveals a nonlinear interplay between finite ion size effects and fixed charge, including the existence of a critical membrane potential at which the influence of permanent charge on the ionic flux reverses sign. These findings highlight novel nonlinear effects arising from finite ion size and permanent charge in ionic flows, and offer insights into biological ion channel behavior that are beyond the reach of current experimental techniques.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Marchenko Method for Soliton Solutions to the Sawada–Kotera Equation","authors":"Tuncay Aktosun,&nbsp;Ramazan Ercan,&nbsp;Ivan Toledo,&nbsp;Mehmet Unlu","doi":"10.1111/sapm.70280","DOIUrl":"https://doi.org/10.1111/sapm.70280","url":null,"abstract":"<div>\u0000 \u0000 <p>Associated with the third-order linear differential operator, we present the Marchenko integral equation using as input the bound-state poles of a transmission coefficient and the time-evolved bound-state dependency constants. We derive the <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$mathbf {N}$</annotation>\u0000 </semantics></math>-soliton solution to the Sawada–Kotera equation, for an arbitrary positive integer <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$mathbf {N}$</annotation>\u0000 </semantics></math>, by recovering that soliton solution from the solution to our Marchenko integral equation. Our method explains the origin of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$2mathbf {N}$</annotation>\u0000 </semantics></math> real parameters appearing in the <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$mathbf {N}$</annotation>\u0000 </semantics></math>-soliton solution formula obtained by the ad-hoc method of Hirota. We show that <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$mathbf {N}$</annotation>\u0000 </semantics></math> of those parameters are related to the <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$mathbf {N}$</annotation>\u0000 </semantics></math> bound-state poles of the left transmission coefficient and the remaining <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$mathbf {N}$</annotation>\u0000 </semantics></math> parameters are related to the bound-state dependency constants. Our Marchenko integral equation corresponds to the “GLM (Gel'fand–Levitan–Marchenko) integral equation” Kaup relentlessly but unsuccessfully tried to obtain.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Complex Nonchaotic Dynamics and Hidden Chaos in 3D Jerk System Without Equilibrium or Infinitely Many Equilibria","authors":"Qigui Yang,&nbsp;Xiaoting Lu","doi":"10.1111/sapm.70279","DOIUrl":"https://doi.org/10.1111/sapm.70279","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper systematically analyzes complex dynamics of a 3D quadratic Jerk system without equilibrium or with infinitely many equilibria, focusing on the generation mechanisms of nonchaotic behaviors and hidden chaos. First, Lyapunov stability of a line of nonhyperbolic equilibria is analyzed. Further, the concept of Jacobi stability is extended to the case where the deviation curvature tensor has a zero eigenvalue, thereby obtaining that a line of nonhyperbolic equilibria is Jacobi unstable for certain parameters. Second, we analyze three special cases: (i) a linear Jerk system for which the induced flow is proved to be weakly Li–Yorke chaos in weak topology and which has infinitely many periodic orbits; (ii) a completely integrable Jerk system, which has a homoclinic orbit and a family of periodic orbits; (iii) a simple nonlinear Jerk system, for which we prove that there exist infinitely many singularly degenerate heteroclinic cycles when invariant algebraic surfaces vanish. Third, we analyze the global dynamics on the invariant algebraic surfaces of Jerk system, covering IMSDHCs, Jacobi stability, and dynamics at infinity. Fourth, we use the averaging theory to prove that a hidden periodic orbit bifurcates from a nonisolated zero-Hopf equilibrium at the origin and nonorigin equilibrium, and establish, based on KAM theorem, the existence of hidden nested invariant tori surrounding this periodic orbit. Meanwhile, there are island chains and hidden chaos near nested invariant tori. Finally, Poincaré map shows that hidden chaos is generated via the Feigenbaum period-doubling route, and its existence is verified based on the topological horseshoe theory with a computer-assisted proof.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local Well-Posedness for Nonlinear Dirac Equation on N-Star Metric Graphs","authors":"Huichao Xing,&nbsp;Zhipeng Yang","doi":"10.1111/sapm.70273","DOIUrl":"https://doi.org/10.1111/sapm.70273","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;We consider the Cauchy problem for the nonlinear Dirac equation on a noncompact &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;annotation&gt;$N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-star metric graph &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;,\u0000\u0000 &lt;/p&gt;&lt;div&gt;&lt;span&gt;&lt;span&gt;&lt;!--FIGURE--&gt;&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$begin{equation*} mathrm{i}partial _t psi = Dpsi - |psi |^{p-2}psi, qquad psi (0)=psi _0, end{equation*}$$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;&lt;/div&gt;where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$pge 3$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$psi:mathbb {R}times Grightarrow mathbb {C}^2$&lt;/annotation&gt;\u0000 &lt;/semantics","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.70284","DOIUrl":"https://doi.org/10.1111/sapm.70284","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70284","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modelling Measles Transmission Dynamics in Madagascar: Mixed Vaccination Strategy and Bifurcation Analysis","authors":"Siyu Liu,&nbsp;Shuai Wang,&nbsp;Yingjie Bi,&nbsp;Jicai Huang","doi":"10.1111/sapm.70277","DOIUrl":"https://doi.org/10.1111/sapm.70277","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we developed and implemented an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>E</mi>\u0000 <mi>I</mi>\u0000 <mi>R</mi>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mi>l</mi>\u0000 </msub>\u0000 <mi>V</mi>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation>$SEIRV_{l}VS$</annotation>\u0000 </semantics></math> model to investigate the transmission dynamics of measles in Madagascar from 2018. A comprehensive sensitivity analysis was conducted to evaluate the impact of key parameters on the basic reproduction number <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathcal {R}_{0}$</annotation>\u0000 </semantics></math>. The data fitting results indicate that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$mathcal {R}_{0}&gt;1$</annotation>\u0000 </semantics></math>, suggesting that measles is likely to resurge in Madagascar despite the observed decline in reported cases. To mitigate this resurgence, we proposed a mixed vaccination strategy for controlling measles transmission in Madagascar. Theoretical analysis demonstrated the existence, local stability and global stability of infection-free periodic solutions. Furthermore, numerical simulations were employed to illustrate the presence of non-trivial periodic solutions. The mixed vaccination strategy framework shows that, with low vaccination coverage and easily achievable vaccination intervals, this strategy can both rapidly contain outbreaks and sustain long-term disease elimination. By integrating theoretical findings with numerical simulations, we gained clearer insights into the effectiveness of the mixed vaccination strategy. This study provides valuable guidance for designing rational prevention and control measures against measles in Madagascar, with potential applications to other regions as well.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical Study of the Sharp Stratification Limit Toward Bilayer Models","authors":"Théo Fradin","doi":"10.1111/sapm.70275","DOIUrl":"https://doi.org/10.1111/sapm.70275","url":null,"abstract":"<div>\u0000 \u0000 <p>In the study of oceanic flows at the geophysical scale, the phenomenon of density stratification plays a central role in the dynamics of the system. Two categories of mathematical models are commonly used to describe the role played by the density stratification: On the one hand, continuously stratified models—such as the stratified Euler equations in a strip, considered in this article—offer an accurate description of vertical effects, but come with a high level of complexity, both at the theoretical and numerical levels. On the other hand, bilayer models approximate the stratification by a piecewise constant profile. In the latter case, the main point is to study the evolution of the free interface between both layers, which leads to a substantially simplified model. In this article, we compare both approaches in the framework of the linearized stratified Euler equations around density profiles that are close to piecewise constant profiles, and prove the convergence toward the bilayer Euler equations. However, in the presence of a shear flow, bilayer models have a range of validity limited by the presence of Kelvin–Helmholtz instabilities. In this case, we use a suitable normal modes decomposition to compute numerically the dispersion relation of this linearized model, and provide numerical evidence that the Kelvin–Helmholtz instabilities limit the applicability of two widely used bilayer models, namely the bilayer Euler equations and the bilayer shallow-water equations.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}